bad round grouping

Give it a good scrubbing then shoot some more then see what it does . Try some other ammo then post the pictures of the targets . Try checking the bedding of the action and if the Barrel is touching the stock . Its only a matter of time till you get it to shoot well. Are you shooting off a solid rest and if so try moving the front rest back an inch or two . What size groups are we talking ? Please give us more details , Pictures are worth a thousand words...lol

My thoughts are stop scrubbing ! You could be cleaning too much and not firing any fouling shots. From a clean barrel fire two fouling shots then try a 5 shot group . Then another 5 shot group and so on . See if the accuracy gets better as more shots are fired and at what point does it start to get worse again. This then gives you the number of shots before you need to clean again .

it has a mid priced scope which I have used before on other rifles with to much drama

Have you used THIS particular scope, or just one of the same model before? Every manufacturer makes a turd now and then. If you've got another scope available, switch it out and see what happens. No need to actually sight it in- just hold the same and check the group. The results will be very evident within only a couple of shots.
Hope it helps!

IMO, if it is truly 4" at 100 meters there is something wrong besides a dirty barrel. You could have over tightened the scope rings and tweaked the scope, especially if they were not lapped. You could have an extremely crappy factory trigger, which would not surprise anyone.

It can't be a dirty barrel as he said he was cleaning every 4 or 5 shots unless the cleaning system is not good enough !
That's over cleaning to be looking for tight groups running in maybe yes . I agree that other things might also be wrong . Scope , mounts , bedding , action screws , ammo change , all needs to be addressed .
Could also be mistakes in shooting technique which includes how the gun is setup and supported .
Could be a combination of a few things working together.

First I would put a new scope on it, I have had issues moving scopes from one rifle to another,
second would be to check the barrel to make sure its not touching the forestock,, also make sure the stock to barrel screw is tight, slide a paper under it,,
Third and hopefully not your problem is what I have with a new savage 308, it just hates factory ammo, ( two scopes later) seems the chamber lead in is just to long and the bullets jumping to get to the lands and they end up with a 2-3 inch group at 100, I am reloading the bullets seating them further out,,,, recommended case over all length was 2.810, I am sub inch groups now with COL at 2.880 Bullet is about .015 back from the lands as best I can tell,,,
under 3 inchs at 300 on a no coffee day